Math  /  Calculus

Question4 Mark for Review - -1 - - - -
If the infinite series n=0an\sum_{n=0}^{\infty} a_{n} diverges, Sn=k=0nakS_{n}=\sum_{k=0}^{n} a_{k}, and limnbn0\lim _{n \rightarrow \infty} b_{n} \neq 0, which of the following statements must be true?
1. limnan0\lim _{n \rightarrow \infty} a_{n} \neq 0
11. limnSn\lim _{n \rightarrow \infty} S_{n} does not exist. II. n=0bn\sum_{n=0}^{\infty} b_{n} diverges. (A) Ionly (B) Il only (C) II and ili only

D I and III only

Studdy Solution
Determine which combination of statements is true.
From the analysis: - Statement I is not necessarily true. - Statement II is true. - Statement III is true.
Thus, the combination of statements II and III is true.
The correct answer is (C) II and III only.

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